
<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable Halliburton Company to comply with the Securities Act of
1933, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in respect thereof, in connection with the registration
under said Securities Act of 1933, as amended, of shares of the Common Stock of
Halliburton Company, par value $2.50 per share, to be sold and offered for sale
pursuant to the terms of the Dresser Industries, Inc. Deferred Compensation Plan
for Non-employee Directors, the Dresser Industries, Inc. Stock Based
Compensation Arrangement for Non-Employee Directors, the Dresser Industries,
Inc. 1982 Stock Option Plan, The 1989 Restricted Incentive Stock Plan, the
Dresser Industries, Inc. 1992 Stock Compensation Plan, the Baroid Corporation
1990 Long Term Performance Incentive Plan, the Wheatley TXT Corp. 1990 Stock
Option Plan, and the Dresser Industries, Inc. Deferred Compensation Plan,
including specifically, but without limitation thereof, power and authority to
sign my name as Director of Halliburton Company to any registration statements
and applications and statements to be filed with the Securities and Exchange
Commission in respect of said shares of Common Stock and all amendments thereto,
including without limitation post-effective amendments thereto, and to any
instruments or documents filed as a part of or in connection therewith; and I
hereby ratify and confirm all that said attorneys or attorney shall do or cause
to be done by virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this 1st day of October, 1998.

                                 /s/ Anne L. Armstrong
                                 ---------------------------------------------
                                     Anne L. Armstrong
<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable Halliburton Company to comply with the Securities Act of
1933, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in respect thereof, in connection with the registration
under said Securities Act of 1933, as amended, of shares of the Common Stock of
Halliburton Company, par value $2.50 per share, to be sold and offered for sale
pursuant to the terms of the Dresser Industries, Inc. Deferred Compensation Plan
for Non-employee Directors, the Dresser Industries, Inc. Stock Based
Compensation Arrangement for Non-Employee Directors, the Dresser Industries,
Inc. 1982 Stock Option Plan, The 1989 Restricted Incentive Stock Plan, the
Dresser Industries, Inc. 1992 Stock Compensation Plan, the Baroid Corporation
1990 Long Term Performance Incentive Plan, the Wheatley TXT Corp. 1990 Stock
Option Plan, and the Dresser Industries, Inc. Deferred Compensation Plan,
including specifically, but without limitation thereof, power and authority to
sign my name as Director of Halliburton Company to any registration statements
and applications and statements to be filed with the Securities and Exchange
Commission in respect of said shares of Common Stock and all amendments thereto,
including without limitation post-effective amendments thereto, and to any
instruments or documents filed as a part of or in connection therewith; and I
hereby ratify and confirm all that said attorneys or attorney shall do or cause
to be done by virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this 2nd day of October, 1998.

                                    /s/ William E. Bradford
                                    ------------------------------------------
                                        William E. Bradford
<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable Halliburton Company to comply with the Securities Act of
1933, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in respect thereof, in connection with the registration
under said Securities Act of 1933, as amended, of shares of the Common Stock of
Halliburton Company, par value $2.50 per share, to be sold and offered for sale
pursuant to the terms of the Dresser Industries, Inc. Deferred Compensation Plan
for Non-employee Directors, the Dresser Industries, Inc. Stock Based
Compensation Arrangement for Non-Employee Directors, the Dresser Industries,
Inc. 1982 Stock Option Plan, The 1989 Restricted Incentive Stock Plan, the
Dresser Industries, Inc. 1992 Stock Compensation Plan, the Baroid Corporation
1990 Long Term Performance Incentive Plan, the Wheatley TXT Corp. 1990 Stock
Option Plan, and the Dresser Industries, Inc. Deferred Compensation Plan,
including specifically, but without limitation thereof, power and authority to
sign my name as Director of Halliburton Company to any registration statements
and applications and statements to be filed with the Securities and Exchange
Commission in respect of said shares of Common Stock and all amendments thereto,
including without limitation post-effective amendments thereto, and to any
instruments or documents filed as a part of or in connection therewith; and I
hereby ratify and confirm all that said attorneys or attorney shall do or cause
to be done by virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this 1st day of October, 1998.

                                 /s/ Lord Clitheroe
                                 ---------------------------------------------
                                     Lord Clitheroe

<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable Halliburton Company to comply with the Securities Act of
1933, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in respect thereof, in connection with the registration
under said Securities Act of 1933, as amended, of shares of the Common Stock of
Halliburton Company, par value $2.50 per share, to be sold and offered for sale
pursuant to the terms of the Dresser Industries, Inc. Deferred Compensation Plan
for Non-employee Directors, the Dresser Industries, Inc. Stock Based
Compensation Arrangement for Non-Employee Directors, the Dresser Industries,
Inc. 1982 Stock Option Plan, The 1989 Restricted Incentive Stock Plan, the
Dresser Industries, Inc. 1992 Stock Compensation Plan, the Baroid Corporation
1990 Long Term Performance Incentive Plan, the Wheatley TXT Corp. 1990 Stock
Option Plan, and the Dresser Industries, Inc. Deferred Compensation Plan,
including specifically, but without limitation thereof, power and authority to
sign my name as Director of Halliburton Company to any registration statements
and applications and statements to be filed with the Securities and Exchange
Commission in respect of said shares of Common Stock and all amendments thereto,
including without limitation post-effective amendments thereto, and to any
instruments or documents filed as a part of or in connection therewith; and I
hereby ratify and confirm all that said attorneys or attorney shall do or cause
to be done by virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this 2nd day of October, 1998.

                                    /s/ Robert L. Crandall
                                    ------------------------------------------
                                        Robert L. Crandall

<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable Halliburton Company to comply with the Securities Act of
1933, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in respect thereof, in connection with the registration
under said Securities Act of 1933, as amended, of shares of the Common Stock of
Halliburton Company, par value $2.50 per share, to be sold and offered for sale
pursuant to the terms of the Dresser Industries, Inc. Deferred Compensation Plan
for Non-employee Directors, the Dresser Industries, Inc. Stock Based
Compensation Arrangement for Non-Employee Directors, the Dresser Industries,
Inc. 1982 Stock Option Plan, The 1989 Restricted Incentive Stock Plan, the
Dresser Industries, Inc. 1992 Stock Compensation Plan, the Baroid Corporation
1990 Long Term Performance Incentive Plan, the Wheatley TXT Corp. 1990 Stock
Option Plan, and the Dresser Industries, Inc. Deferred Compensation Plan,
including specifically, but without limitation thereof, power and authority to
sign my name as Director of Halliburton Company to any registration statements
and applications and statements to be filed with the Securities and Exchange
Commission in respect of said shares of Common Stock and all amendments thereto,
including without limitation post-effective amendments thereto, and to any
instruments or documents filed as a part of or in connection therewith; and I
hereby ratify and confirm all that said attorneys or attorney shall do or cause
to be done by virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this 30th day of September, 1998.

                                    /s/ Charles J. DiBona
                                    ------------------------------------------
                                        Charles J. DiBona
<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable Halliburton Company to comply with the Securities Act of
1933, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in respect thereof, in connection with the registration
under said Securities Act of 1933, as amended, of shares of the Common Stock of
Halliburton Company, par value $2.50 per share, to be sold and offered for sale
pursuant to the terms of the Dresser Industries, Inc. Deferred Compensation Plan
for Non-employee Directors, the Dresser Industries, Inc. Stock Based
Compensation Arrangement for Non-Employee Directors, the Dresser Industries,
Inc. 1982 Stock Option Plan, The 1989 Restricted Incentive Stock Plan, the
Dresser Industries, Inc. 1992 Stock Compensation Plan, the Baroid Corporation
1990 Long Term Performance Incentive Plan, the Wheatley TXT Corp. 1990 Stock
Option Plan, and the Dresser Industries, Inc. Deferred Compensation Plan,
including specifically, but without limitation thereof, power and authority to
sign my name as Director of Halliburton Company to any registration statements
and applications and statements to be filed with the Securities and Exchange
Commission in respect of said shares of Common Stock and all amendments thereto,
including without limitation post-effective amendments thereto, and to any
instruments or documents filed as a part of or in connection therewith; and I
hereby ratify and confirm all that said attorneys or attorney shall do or cause
to be done by virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this 1st day of October, 1998.

                                 /s/ Lawrence S. Eagleburger
                                 ---------------------------------------------
                                     Lawrence S. Eagleburger
<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable Halliburton Company to comply with the Securities Act of
1933, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in respect thereof, in connection with the registration
under said Securities Act of 1933, as amended, of shares of the Common Stock of
Halliburton Company, par value $2.50 per share, to be sold and offered for sale
pursuant to the terms of the Dresser Industries, Inc. Deferred Compensation Plan
for Non-employee Directors, the Dresser Industries, Inc. Stock Based
Compensation Arrangement for Non-Employee Directors, the Dresser Industries,
Inc. 1982 Stock Option Plan, The 1989 Restricted Incentive Stock Plan, the
Dresser Industries, Inc. 1992 Stock Compensation Plan, the Baroid Corporation
1990 Long Term Performance Incentive Plan, the Wheatley TXT Corp. 1990 Stock
Option Plan, and the Dresser Industries, Inc. Deferred Compensation Plan,
including specifically, but without limitation thereof, power and authority to
sign my name as Director of Halliburton Company to any registration statements
and applications and statements to be filed with the Securities and Exchange
Commission in respect of said shares of Common Stock and all amendments thereto,
including without limitation post-effective amendments thereto, and to any
instruments or documents filed as a part of or in connection therewith; and I
hereby ratify and confirm all that said attorneys or attorney shall do or cause
to be done by virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this 30th day of September, 1998.

                                 /s/ W. R. Howell
                                 ---------------------------------------------
                                     W. R. Howell
<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable Halliburton Company to comply with the Securities Act of
1933, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in respect thereof, in connection with the registration
under said Securities Act of 1933, as amended, of shares of the Common Stock of
Halliburton Company, par value $2.50 per share, to be sold and offered for sale
pursuant to the terms of the Dresser Industries, Inc. Deferred Compensation Plan
for Non-employee Directors, the Dresser Industries, Inc. Stock Based
Compensation Arrangement for Non-Employee Directors, the Dresser Industries,
Inc. 1982 Stock Option Plan, The 1989 Restricted Incentive Stock Plan, the
Dresser Industries, Inc. 1992 Stock Compensation Plan, the Baroid Corporation
1990 Long Term Performance Incentive Plan, the Wheatley TXT Corp. 1990 Stock
Option Plan, and the Dresser Industries, Inc. Deferred Compensation Plan,
including specifically, but without limitation thereof, power and authority to
sign my name as Director of Halliburton Company to any registration statements
and applications and statements to be filed with the Securities and Exchange
Commission in respect of said shares of Common Stock and all amendments thereto,
including without limitation post-effective amendments thereto, and to any
instruments or documents filed as a part of or in connection therewith; and I
hereby ratify and confirm all that said attorneys or attorney shall do or cause
to be done by virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this 1st day of October, 1998.

                                 /s/ Ray L. Hunt
                                 ---------------------------------------------
                                     Ray L. Hunt
<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable Halliburton Company to comply with the Securities Act of
1933, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in respect thereof, in connection with the registration
under said Securities Act of 1933, as amended, of shares of the Common Stock of
Halliburton Company, par value $2.50 per share, to be sold and offered for sale
pursuant to the terms of the Dresser Industries, Inc. Deferred Compensation Plan
for Non-employee Directors, the Dresser Industries, Inc. Stock Based
Compensation Arrangement for Non-Employee Directors, the Dresser Industries,
Inc. 1982 Stock Option Plan, The 1989 Restricted Incentive Stock Plan, the
Dresser Industries, Inc. 1992 Stock Compensation Plan, the Baroid Corporation
1990 Long Term Performance Incentive Plan, the Wheatley TXT Corp. 1990 Stock
Option Plan, and the Dresser Industries, Inc. Deferred Compensation Plan,
including specifically, but without limitation thereof, power and authority to
sign my name as Director of Halliburton Company to any registration statements
and applications and statements to be filed with the Securities and Exchange
Commission in respect of said shares of Common Stock and all amendments thereto,
including without limitation post-effective amendments thereto, and to any
instruments or documents filed as a part of or in connection therewith; and I
hereby ratify and confirm all that said attorneys or attorney shall do or cause
to be done by virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this 30th day of September, 1998.

                                    /s/ Jay A. Precourt
                                    ------------------------------------------
                                        Jay A. Precourt
<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable Halliburton Company to comply with the Securities Act of
1933, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in respect thereof, in connection with the registration
under said Securities Act of 1933, as amended, of shares of the Common Stock of
Halliburton Company, par value $2.50 per share, to be sold and offered for sale
pursuant to the terms of the Dresser Industries, Inc. Deferred Compensation Plan
for Non-employee Directors, the Dresser Industries, Inc. Stock Based
Compensation Arrangement for Non-Employee Directors, the Dresser Industries,
Inc. 1982 Stock Option Plan, The 1989 Restricted Incentive Stock Plan, the
Dresser Industries, Inc. 1992 Stock Compensation Plan, the Baroid Corporation
1990 Long Term Performance Incentive Plan, the Wheatley TXT Corp. 1990 Stock
Option Plan, and the Dresser Industries, Inc. Deferred Compensation Plan,
including specifically, but without limitation thereof, power and authority to
sign my name as Director of Halliburton Company to any registration statements
and applications and statements to be filed with the Securities and Exchange
Commission in respect of said shares of Common Stock and all amendments thereto,
including without limitation post-effective amendments thereto, and to any
instruments or documents filed as a part of or in connection therewith; and I
hereby ratify and confirm all that said attorneys or attorney shall do or cause
to be done by virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this 1st day of October, 1998.

                                    /s/ Delano E. Lewis
                                    ------------------------------------------
                                        Delano E. Lewis
<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable Halliburton Company to comply with the Securities Act of
1933, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in respect thereof, in connection with the registration
under said Securities Act of 1933, as amended, of shares of the Common Stock of
Halliburton Company, par value $2.50 per share, to be sold and offered for sale
pursuant to the terms of the Dresser Industries, Inc. Deferred Compensation Plan
for Non-employee Directors, the Dresser Industries, Inc. Stock Based
Compensation Arrangement for Non-Employee Directors, the Dresser Industries,
Inc. 1982 Stock Option Plan, The 1989 Restricted Incentive Stock Plan, the
Dresser Industries, Inc. 1992 Stock Compensation Plan, the Baroid Corporation
1990 Long Term Performance Incentive Plan, the Wheatley TXT Corp. 1990 Stock
Option Plan, and the Dresser Industries, Inc. Deferred Compensation Plan,
including specifically, but without limitation thereof, power and authority to
sign my name as Director of Halliburton Company to any registration statements
and applications and statements to be filed with the Securities and Exchange
Commission in respect of said shares of Common Stock and all amendments thereto,
including without limitation post-effective amendments thereto, and to any
instruments or documents filed as a part of or in connection therewith; and I
hereby ratify and confirm all that said attorneys or attorney shall do or cause
to be done by virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this 1st day of October, 1998.

                                 /s/ C. J. Silas
                                 --------------------------------------------
                                     C. J. Silas
<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable Halliburton Company to comply with the Securities Act of
1933, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in respect thereof, in connection with the registration
under said Securities Act of 1933, as amended, of shares of the Common Stock of
Halliburton Company, par value $2.50 per share, to be sold and offered for sale
pursuant to the terms of the Dresser Industries, Inc. Deferred Compensation Plan
for Non-employee Directors, the Dresser Industries, Inc. Stock Based
Compensation Arrangement for Non-Employee Directors, the Dresser Industries,
Inc. 1982 Stock Option Plan, The 1989 Restricted Incentive Stock Plan, the
Dresser Industries, Inc. 1992 Stock Compensation Plan, the Baroid Corporation
1990 Long Term Performance Incentive Plan, the Wheatley TXT Corp. 1990 Stock
Option Plan, and the Dresser Industries, Inc. Deferred Compensation Plan,
including specifically, but without limitation thereof, power and authority to
sign my name as Director of Halliburton Company to any registration statements
and applications and statements to be filed with the Securities and Exchange
Commission in respect of said shares of Common Stock and all amendments thereto,
including without limitation post-effective amendments thereto, and to any
instruments or documents filed as a part of or in connection therewith; and I
hereby ratify and confirm all that said attorneys or attorney shall do or cause
to be done by virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this 30th day of September, 1998.

                                    /s/ Richard J. Stegemeier
                                    -----------------------------------------
                                        Richard J. Stegemeier
<PAGE>
 
                                                                    EXHIBIT 24.1

                               POWER OF ATTORNEY

     KNOW ALL MEN BY THESE PRESENTS, that I, the undersigned, a Director of
Halliburton Company, do hereby constitute and appoint David J. Lesar, Lester L.
Coleman, Gary V. Morris and Susan S. Keith, or any of them acting alone, my true
and lawful attorneys or attorney, to do any and all acts and things and execute
any and all instruments which said attorneys or attorney may deem necessary or
advisable to enable Halliburton Company to comply with the Securities Act of
1933, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in respect thereof, in connection with the registration
under said Securities Act of 1933, as amended, of shares of the Common Stock of
Halliburton Company, par value $2.50 per share, to be sold and offered for sale
pursuant to the terms of the Dresser Industries, Inc. Deferred Compensation Plan
for Non-employee Directors, the Dresser Industries, Inc. Stock Based
Compensation Arrangement for Non-Employee Directors, the Dresser Industries,
Inc. 1982 Stock Option Plan, The 1989 Restricted Incentive Stock Plan, the
Dresser Industries, Inc. 1992 Stock Compensation Plan, the Baroid Corporation
1990 Long Term Performance Incentive Plan, the Wheatley TXT Corp. 1990 Stock
Option Plan, and the Dresser Industries, Inc. Deferred Compensation Plan,
including specifically, but without limitation thereof, power and Authority to
sign my name as Director of Halliburton Company to any registration statements
and applications and statements to be filed with the Securities and Exchange
Commission in respect of said shares of Common Stock and all amendments thereto,
including without limitation post-effective amendments thereto, and to any
instruments or documents filed as a part of or in connection therewith; and I
hereby ratify and confirm all that said attorneys or attorney shall do or cause
to be done by virtue hereof.

     IN TESTIMONY HEREOF, witness my hand this 1st day of October, 1998.

                                    /s/ J. Landis Martin
                                    ------------------------------------------
                                        J. Landis Martin
